Heightmap on sphere gives a weird equator
Sorry this answer only the "is there another way to do this". Check out @Cegaton comments for pointers to ways to fix your problem.

Since your texture seems to be Equirectangular (tell me if I am wrong), you can use Environment texture node which can be used directly on an sphere or icosphere without manual UV mapping. 

The example below uses cycles adaptive subdiv modifier (requires experimental features enabled). This works also with regular bump displacement with Cycles and Eevee.